Multifidelity modeling in support of design and uncertainty quantification

Sponsored by the AIAA MDO Technical Committee

Held in conjunction with AIAA AVIATION 2019

Hilton Anatole, Dallas TX

Sunday June 16, 2019


Multifidelity Modeling (MFM) Workshop

Multifidelity modeling encompasses a broad range of methods that use approximate models together with high-fidelity models to accelerate a computational task that requires repeated model evaluations. This workshop will highlight the tremendous recent progress of multifidelity methods for design optimization and uncertainty quantification, including (but not limited to) methods based on adaptive sampling, control variate formulations, importance sampling, trust region model management, model fusion, and Bayesian optimization. The focus is on a tutorial-style series of lectures aimed at the practitioner, together with forward-looking discussions of challenges and opportunities. The workshop will include the following key discussion topics: 1) multifidelity formulations that combine computational models with other sources of information, such as experimental data and expert opinion; 2) exploiting the connections between multifidelity modeling and machine learning methods; 3) past successes of applying multifidelity modeling in aircraft design, structural modeling, and other fields; 4) future opportunities in areas such as material design and autonomous systems.

Objectives: 1) Dissemination of recent methods developments to the MDO practitioner community. 2) Discussion of challenges and opportunities to identify new collaborations and new research directions.

Held in conjunction with AIAA AVIATION 2019

Room info: Senators Lecture Hall, which is located on the Lobby Level of the hotel in the Tower area (close to the elephants).

Hilton Anatole, Dallas TX

Sunday June 16, 2019

Workshop Schedule

16 June, 2019

08 : 00 AM - 08 : 15 AM


08 : 15 AM - 09 : 25 AM

Tutorial 1: Metamodeling / Surrogate Modeling / Machine Learning

By Matthias Poloczek (University of Arizona)

Bayesian optimization (BO) has recently been applied with great success to global optimization of expensive-to-evaluate functions in machine learning, engineering, healthcare, and other areas. While traditional BO methods only query the expensive-to-evaluate objective, we also often have access to other information sources: when optimizing an aerodynamic design, we may assess its performance by wind tunnel studies, or by CFD simulations with varying mesh sizes; when optimizing an inventory management system, we may evaluate it in real life at the client’s warehouse, or by discrete-event simulations that vary in length and number of replications. These approximations are typically subject to an unknown bias in addition to common noise. This so-called model discrepancy results from an inherent inability to model the reality accurately, e.g., due to limited physical models. This tutorial will provide an introduction to Bayesian optimization: we will show how to build a surrogate for the unknown objective function via Gaussian process regression that allows to quantify the uncertainty in the surrogate. Then we will survey techniques to decide where to evaluate the function in order to find a global optimizer. In the second part of the tutorial we extend the BO methodology to multiple information sources, demonstrating substantial reduction of optimization cost for applications in machine learning and aerospace engineering. Time permitting, we will also discuss other applications of BO in aerospace engineering, e.g., sparsification of couplings in an aerostructural multi-component model.

Links to related software packages: 1) misoKG Algorithm for Multifidelity Bayesian Optimization; 2) A Python Library for Parallel Bayesian Optimization Algorithms; and 3) BoTorch: Bayesian Optimization in PyTorch

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09 : 25 AM - 09 : 40 AM


09 : 40 AM - 10 : 50 AM

Tutorial 2: Multifidelity Optimization / Surrogate-based Optimization

By Felipe Viana (University of Central Florida)

In multifidelity optimization, the simulations from multiple physics fidelity levels are usually modeled through surrogate methods such as the Gaussian process. It is true that the end goal is to solve the optimization problem. However, the inherent need of a surrogate connecting the simulation models also brings additional challenges such as model refinement through sequential sampling, data and model uncertainty, and availability (and use) of gradients. This tutorial will (a) give an overview on motivation and historical aspects of multifidelity optimization, (b) review established methods for multifidelity optimization, (c) discuss how Bayesian statistics enables optimization with multiple sources of data, (d) give few examples of recent developments and promising research, and (e) discuss opportunities for multifidelity optimization using physics-informed machine learning.

Links to related software packages: 1) Gaussian Process Models for Simulation Analysis (GPM/SA); 2) Dakota; 3) Queso Library; and 4) Physics-informed neural networks (PINN)

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10 : 50 AM - 12 : 00 PM

Tutorial 3: Multifidelity Uncertainty Quantification

By Benjamin Peherstorfer (New York University)

Uncertainty quantification with sampling-based methods such as Monte Carlo can require a large number of numerical simulations of models describing the systems of interest to obtain estimates with acceptable accuracies. Thus, if a computationally expensive high-fidelity model is used alone, Monte-Carlo-based uncertainty quantification methods quickly become intractable. In this tutorial presentation, we survey recent advances in multifidelity methods for sampling-based uncertainty quantification. The goal of the multifidelity methods that we discuss is to significantly speedup uncertainty quantification by leveraging low-cost low-fidelity models while establishing accuracy guarantees and unbiasedness via occasional recourse to the expensive high-fidelity models. We survey methods for (a) uncertainty propagation, (b) rare event simulation, (c) sensitivity analysis, and (d) Bayesian inverse problems. If time permits, we will (e) give an outlook to context-aware learning of data-driven low-fidelity models, where models are learned explicitly for improving the performance of multifidelity computations rather than providing accurate approximations of high-fidelity models.

Links to related software package: Multi Fidelity Monte Carlo

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12 : 00 PM - 01 : 30 PM


01 : 30 PM - 03 : 00 PM

Panel: User Stories, Success Cases and Target Areas

Panel Chair: Laura Mainini (UTRC), and Michael C Henson (Lockheed Martin Corporation)

Panel Members: Mike Eldred (Sandia National Laboratories), Andy Ko (Phoenix Integration), Vlaidimir Balabanov (The Boeing Company), and Matteo Diez (CNR-INM)

Mike Eldred

In the simulation of complex physics, multiple model forms of varying fidelity and resolution are commonly available. In computational fluid dynamics, for example, common model fidelities include potential flow, inviscid Euler, Reynolds-averaged Navier Stokes, and large eddy simulation, each potentially supporting a variety of spatio-temporal resolution/discretization settings. While we seek results that are consistent with the highest fidelity, the computational cost of performing UQ exclusively with this model quickly becomes prohibitive. By leveraging information from multiple fidelities and resolutions, however, resources can be carefully allocated across these information sources, minimizing computational cost while addressing multiple sources of error (deterministic bias, stochastic estimator variance, emulator error, etc.). In this presentation, I will briefly overview our approaches for multifidelity modeling, including both sampling and surrogate approaches. I will then present experiences working with model problems, aerospace applications (nozzles and scramjets), and energy (wind, tokamaks). Performance on realistic engineering applications indicates significant promise, but also points to significant R&D needs when moving beyond elliptic PDEs.

Andy Ko

Phoenix Integration has been enabling the use of MDO in industry for the last 20 years. The presentation will discuss our origins, where we are today, and what the plans are for the future. We will highlight the future challenges, as well as opportunities that we see coming. Success stories with the application of MDO will also be presented. Lastly, we will talk about our current initiatives to remain at the cutting edge of multidisciplinary integration and optimization.

Vlaidimir Balabanov

Multifidelity modeling is an important element in aircraft design and optimization: selecting models with appropriate fidelity for the given design, synthesizing multifidelity information, enabling uncertainty quantification. Mutifidelity modeling certainly helps to support uncertainty quantification. But doesn’t resolve all the issues. Rather than suggesting answers, the questions will be asked during the presentation that are of immediate practical interest to industry. With the hope of either getting answers or enabling interest to work on them. Some of the questions are: (a) Generating composite allowables efficient – should the tests be combined with FE and how? (b) Robust Optimization of complex systems – are the models good enough to estimate 6 sigma? (c) Methodology to reduce the probability of redesign. (d) Efficiently dealing with a curse of dimensionality for uncertainty quantification.

Matteo Diez

Challenges and opportunities in design and uncertainty quantification of watercrafts: where sea and sky meet. The technological challenges associated to design and uncertainty quantification of ships and watercrafts will be presented, focusing on similarities to aeronautics as well as peculiar aspects. The use of adaptive multifidelity modeling will be discussed to select the proper equations/solver/grid for performance analysis, optimization, and uncertainty quantification, along with reduced-dimensionality representations of design/operational spaces. The shape optimization of a naval destroyer in realistic operations/environment will be shown. Examples will be presented of joint efforts of researchers from sea and air areas within the context of NATO AVT (Applied Vehicle Technology) research groups.

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03 : 00 PM - 03 : 30 PM


03 : 30 PM - 05 : 00 PM (20 mins each talk)

New and Exciting Research Directions

Talks by: Seongim Choi (Virginia Tech), Rhea P. Liem (The Hong Kong University of Science and Technology), Nathalie Bartoli (ONERA), and Rahul Rai (University at Buffalo)

"Multiple response GPR model for multidisciplinary analysis and design" by Seongim Choi

Variable-fidelity analysis and design (VFAD) is a practical tool of great importance by yielding high accuracy at reduced computational cost. The method is particularly significant for the conceptual design of complex and large-scale aerospace system. We introduce a multiple response Gaussian process regression model to design a system, where multiple physics are strongly coupled and high-fidelity physics simulation takes considerable time. Issues that determine the success of the design will be discussed as follows: 1) how many high- and/or low-fidelity function analyses are desired, 2) where in the design space high- or low-fidelity function analyses should be applied, 3) what is the level of fidelity needed to evaluate design candidates or additional samples, and 4) how well the coupling interfaces are modeled for multiple output responses.

"Data-enhanced modeling for air transportation applications" by Rhea P Liem

Despite the advancement of computational methods and numerical techniques, a realistic and accurate representation of a complex system is still hard to attain. Uncertainties and variations in the operating conditions impose challenges in the modeling. Designers and decision makers often resolve to simplify the representation of the physics, or work within the boundary of some prescribed assumptions. When these analysis results are used in important decision-making analyses, the inaccuracies might have some undesirable implications. In this talk, I will discuss how we can incorporate some actual data to improve the models and make them more realistic. Some examples focusing on air transportation applications will be presented.

"Bayesian optimization of an airfoil shape design via multi-fidelity surrogate modeling" by Nathalie Bartoli

In a context of optimization with multiple information sources with varying degrees of fidelity, with varying associated accuracy and querying costs, we propose to formulate a multi-fidelity extension for Efficient Global Optimization in the context of airfoil shape optimization using both a RANS solver and a low fidelity approximation based on a simplified physical formulation. The new developments based on Bayesian optimization and kriging metamodeling allow the aerodynamic optimization to be sped up and divide for example (on a 15-design-variable unconstrained optimization problem) the total cost by at least two compared to a single fidelity optimization.

"Physics LEArning (PLEA): A Hybrid Physics Guided Machine Learning Approach for Predictive Modeling of Complex Systems" by Rahul Rai

Integrating simplified or partial physics models with data-driven models (e.g., deep neural networks (DNN)) is an emerging concept, targeted at facilitating generalizability and extrapolability of complex system behavior predictions. In this talk, I will introduce ideas related to hybrid models that enable the integration of first principle Physics-Based Models and machine learning (ML) models. Various hybrid architecture variants in which the output of the partial physics is infused as an input at various layers of a DNN will be discussed. Examples will be provided to showcase that the proposed hybrid architectures ensure better generalizability beyond their initial set of training data. DARPA funding supports this work.

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AIAA Member - Early (until 27 May) $190

AIAA Member - Standard $290

Conference Rate $390


Organizing Team

Douglas Allaire

Texas A&M

Karen Willcox

UT Austin

Laura Mainini


Leifur Leifsson

Iowa State University

Michael C. Henson

Lockheed Martin Corp.

Souma Chowdhury

University at Buffalo

Vassili Toropov

Queen Mary U of London

Contact Info